A Simple Hybrid Variance Estimator for the Kaplan-Meier Survival Function

• Activity Number: 112
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Craig B. Borkowf*+
• Companies: Centers for Disease Control and Prevention
• Keywords: clinical trial ; Kaplan-Meier survival function ; Greenwood variance estimator ; Peto variance estimator ; simulation study ; survival analysis

Abstract

We propose a new hybrid variance estimator for the Kaplan-Meier survival function. This new estimator approximates the true variance by a binomial variance formula, where the proportion parameter is a piecewise nonincreasing function of the KM survival function and its upper bound. Also, the effective sample size equals the number of subjects not censored prior to that time. In addition, we consider an adjusted hybrid variance estimator that modifies the regular estimator for small sample sizes. We present a simulation study to compare the performance of the regular and adjusted hybrid variance estimators to the Greenwood and Peto variance estimators for small sample sizes. We show that the new variance estimators give better variance estimates and confidence intervals with more nominal coverage rates than the traditional variance estimators. Indeed, the Greenwood and Peto variance estimators can substantially underestimate the true variance in the left and right tails of the survival distribution, even with moderately censored data. Finally, we illustrate the use of these new and traditional variance estimators on an example from a leukemia clinical trial.